1.5.1 is an update which mainly fixed issues with low frame rates on certain devices. As the protocol is the same as 1.5, players on 1.5.1 can connect to servers that are running 1.5. While it was not the last update to 1.5, it was the last one before the snapshots of 1.6.1 started.
MC-250 – Ender Dragon can still grief stuff like cobblestone and chests even if the gamerule mobGriefing is set on false.
MC-4577 – Unable to combine enchanted books for a higher level enchant.
MC-6391 – Fire on hopper not visible
MC-6705 – If you use an external editing tool (MCEdit) to give an enchanted book with multiple enchantments, and you try to combine it with an item, it will only enchant it with the first enchantment on the list.
MC-8193 – Hopper doesn't try to place items from other slots if unable from first.
MC-8824 – FPS Drop due to Smooth Lighting
MC-8943 – Fire doesn't show on 8 layered snow and hopper
MC-11089 – Long scoreboard objective titles can be offset screen
MC-11109 – Breaking a Container with Items that is connected via a solid block with a Comparator does not update the Comparator
MC-11217 – Falling Block entities start visually falling from 1 block higher than they were placed
MC-11236 – Paintings popping out / cannot place new ones
MC-11654 – The text of things fall out of the picture